Physics · Optics

Optics formulas for JEE

Every Optics formula you need for JEE, grouped by concept.

FormulasRevision notes
55 formulas8 concepts
01Reflection of Light02Refraction of Light03Dispersion and Scattering04Optical Instruments05Wavefront and Huygens' Principle06Interference07Diffraction08Polarisation
01

Reflection of Light

4 formulas

Linear Magnification (Mirror)

m=h′h=−vum = \frac{h'}{h} = -\frac{v}{u}

Ratio of image height to object height for spherical mirrors.

applies whenTransverse object/image.
reflectionmirrormagnification

Mirror Equation

1v+1u=1f\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

Relation between object distance, image distance, and focal length for spherical mirrors.

applies whenParaxial rays, Cartesian sign convention applies.
reflectionmirrorequation

Focal Length of Spherical Mirror

f=R2f = \frac{R}{2}

Relation between focal length and radius of curvature for paraxial rays.

applies whenParaxial rays only.
reflectionmirrorfocal_length

Longitudinal Velocity of Image in Mirror

vimage=−m2vobjectv_{image} = -m^2 v_{object}

Velocity of the image along the principal axis when the object is moving towards/away from the mirror.

applies whenMirror is at rest.
reflectionmirrorvelocityjee-advanced
02

Refraction of Light

15 formulas

Apparent Depth

happ=hrealnrelh_{app} = \frac{h_{real}}{n_{rel}}

Apparent depth of an object in a denser medium viewed from a rarer medium.

applies whenNear-normal viewing.
refractiondepth

Displacement Method for Convex Lens

f=D2−x24Df = \frac{D^2 - x^2}{4D}

Finding focal length by moving a convex lens between two fixed pins.

applies whenD≥4fD \geq 4f
refractionlensexperimentjee-advanced

Lateral Shift

x=tsin⁡(i−r)cos⁡rx = \frac{t \sin(i - r)}{\cos r}

Lateral displacement of a ray emerging from a parallel-sided glass slab.

applies whenParallel slab of thickness t.
refractionslabshiftjee-advanced

Thin Lens Formula

1v−1u=1f\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

Relation between object distance, image distance, and focal length for thin lenses.

applies whenThin lens, paraxial rays.
refractionlensequation

Focal Length of Lens Combination

1f=1f1+1f2+…\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} + \dots

Equivalent focal length of thin lenses placed in contact.

applies whenThin lenses in direct contact.
refractionlensfocal_lengthcombination

Lens Maker's Formula

1f=(n21−1)(1R1−1R2)\frac{1}{f} = (n_{21} - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right)

Calculates focal length of a thin lens based on radii of curvature and relative refractive index.

applies whenThin lens surrounded by uniform medium.
refractionlensfocal_length

Magnification of Lens Combination

m=m1m2m3…m = m_1 m_2 m_3 \dots

Total linear magnification of a combination of lenses.

refractionlensmagnificationcombination

Linear Magnification (Lens)

m=vum = \frac{v}{u}

Ratio of image height to object height for lenses.

applies whenTransverse object/image.
refractionlensmagnification

Newton's Lens Formula

x1x2=f2x_1 x_2 = f^2

Relation between object and image distances measured from the principal foci.

applies whenMeasurements from foci, not optical center.
refractionlensnewtonjee-advanced

Power of a Lens

P=1fP = \frac{1}{f}

Measure of convergence or divergence introduced by a lens.

applies whenf must be in meters for P to be in Dioptres.
refractionlenspower

Power of Lens Combination

P=P1+P2+P3+…P = P_1 + P_2 + P_3 + \dots

Equivalent power of multiple thin lenses in contact.

applies whenThin lenses in direct contact.
refractionlenspowercombination

Equivalent Power of Silvered Lens

Peq=2PL+PMP_{eq} = 2P_L + P_M

Equivalent power when one surface of a lens is silvered, acting as a mirror.

refractionlensmirrorjee-advanced

Snell's Law of Refraction

sin⁡isin⁡r=n21=n2n1=v1v2\frac{\sin i}{\sin r} = n_{21} = \frac{n_2}{n_1} = \frac{v_1}{v_2}

Relation between angles of incidence and refraction, and the relative refractive index.

refractionsnellrefractive_index

Refraction at Spherical Surface

n2v−n1u=n2−n1R\frac{n_2}{v} - \frac{n_1}{u} = \frac{n_2 - n_1}{R}

Relation for refraction across a single curved interface.

applies whenParaxial rays, small aperture.
refractionspherical_surface

Critical Angle for Total Internal Reflection

sin⁡ic=n21=n2n1\sin i_c = n_{21} = \frac{n_2}{n_1}

The angle of incidence above which total internal reflection occurs.

applies whenLight traveling from denser to rarer medium (n1>n2n_1 > n_2).
refractiontircritical_angle
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03

Dispersion and Scattering

5 formulas

Dispersive Power of Prism

ω=nv−nrny−1\omega = \frac{n_v - n_r}{n_y - 1}

Measure of the ability of the material of a prism to disperse light.

applies whenThin prism approximation.
dispersionprismpowerjee-advanced

Prism Internal Angles Relation

r1+r2=Ar_1 + r_2 = A

Sum of angles of refraction at the two interfaces equals the prism angle.

dispersionprismangle

Angle of Deviation (Prism)

δ=i+e−A\delta = i + e - A

Total angle of deviation for a ray passing through a prism.

dispersionprismdeviation

Minimum Deviation (Prism)

n21=sin⁡((A+Dm)/2)sin⁡(A/2)n_{21} = \frac{\sin((A+D_m)/2)}{\sin(A/2)}

Refractive index in terms of angle of minimum deviation and prism angle.

applies whenMinimum deviation case: i=ei = e and r1=r2r_1 = r_2.
dispersionprismminimum_deviation

Deviation by Thin Prism

Dm≈(n21−1)AD_m \approx (n_{21} - 1)A

Deviation angle for prisms with very small refracting angle.

applies whenSmall prism angle A.
dispersionprismthin
04

Optical Instruments

9 formulas

Compound Microscope Magnification (Infinity)

m=Lfo×Dfem = \frac{L}{f_o} \times \frac{D}{f_e}

Magnifying power of a compound microscope in normal adjustment.

applies whenFinal image at infinity.
instrumentsmicroscopecompound

Compound Microscope Magnification (Near Point)

m=vouo(1+Dfe)m = \frac{v_o}{u_o} \left(1 + \frac{D}{f_e}\right)

Magnifying power of a compound microscope with final image at D.

applies whenFinal image at near point D.
instrumentsmicroscopecompoundjee-advanced

Simple Microscope Magnification (Infinity)

m=Dfm = \frac{D}{f}

Angular magnification when the image is formed at infinity.

applies whenRelaxed viewing (image at infinity).
instrumentsmicroscopeinfinity

Simple Microscope Magnification (Near Point)

m=1+Dfm = 1 + \frac{D}{f}

Angular magnification when the image is formed at the near point.

applies whenImage formed at D = 25 cm.
instrumentsmicroscopenear_point

Resolving Power of Microscope

RP=2nsin⁡θ1.22λRP = \frac{2n\sin\theta}{1.22\lambda}

Resolving power limit for a microscope based on numerical aperture.

instrumentsmicroscoperesolving_powerjee-advanced

Resolving Power of Telescope

RP=D1.22λRP = \frac{D}{1.22\lambda}

Resolving power limit set by diffraction of the objective lens aperture.

applies whenAperture diameter D.
instrumentstelescoperesolving_powerjee-advanced

Telescope Magnification (Normal Adjustment)

m=fofem = \frac{f_o}{f_e}

Magnifying power of a refracting astronomical telescope.

applies whenFinal image at infinity (normal adjustment).
instrumentstelescopeinfinity

Telescope Tube Length

L=fo+feL = f_o + f_e

Length of the telescope tube in normal adjustment.

applies whenFinal image at infinity.
instrumentstelescopelength

Telescope Magnification (Near Point)

m=fofe(1+feD)m = \frac{f_o}{f_e}\left(1 + \frac{f_e}{D}\right)

Magnifying power of a telescope when final image is at near point.

applies whenFinal image at near point D.
instrumentstelescopenear_pointjee-advanced
05

Wavefront and Huygens' Principle

2 formulas

Huygens' Refraction Proof

sin⁡isin⁡r=v1v2\frac{\sin i}{\sin r} = \frac{v_1}{v_2}

Ratio of sines of angles equals the ratio of phase speeds in the media.

huygensrefractionvelocity

Refractive Index vs Speed

n=cvn = \frac{c}{v}

Absolute refractive index defined by the ratio of speed of light in vacuum to speed in medium.

huygensrefractionspeed
06

Interference

13 formulas

Constructive Interference (Path Difference)

Δx=nλ\Delta x = n\lambda

Condition for path difference to yield a bright fringe (maxima).

applies whenn=0,±1,±2,…n = 0, \pm 1, \pm 2, \dots
interferenceconstructivepath

Destructive Interference (Path Difference)

Δx=(n+12)λ\Delta x = \left(n + \frac{1}{2}\right)\lambda

Condition for path difference to yield a dark fringe (minima).

applies whenn=0,±1,±2,…n = 0, \pm 1, \pm 2, \dots
interferencedestructivepath

General Interference Intensity

I=I1+I2+2I1I2cos⁡ϕI = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi

Resultant intensity for superposition of coherent waves of any amplitude.

applies whenCoherent sources.
interferenceintensityjee-advanced

Interference Intensity (Equal Amplitudes)

I=4I0cos⁡2(ϕ2)I = 4I_0 \cos^2\left(\frac{\phi}{2}\right)

Resultant intensity for interference of two waves of equal intensity I0.

applies whenCoherent sources of identical intensity.
interferenceintensity

Phase-Path Difference Relation

Δϕ=2πλΔx\Delta \phi = \frac{2\pi}{\lambda} \Delta x

Conversion between phase difference and path difference.

interferencephasepathjee-advanced

Plane Wave Equation

y(x,t)=asin⁡(kx−ωt)y(x,t) = a \sin(kx - \omega t)

Mathematical description of a propagating transverse harmonic wave.

applies when1D propagation along +x.
interferencewave_equation

Superposition of Two Waves

y=2acos⁡(ϕ2)cos⁡(ωt+ϕ2)y = 2a \cos\left(\frac{\phi}{2}\right) \cos\left(\omega t + \frac{\phi}{2}\right)

Resultant displacement from two coherent waves of equal amplitude 'a' and phase difference phi.

applies whenEqual amplitude coherent sources.
interferencesuperposition

Wave Vector

k=2πλk = \frac{2\pi}{\lambda}

Relation between angular wavenumber and wavelength.

interferencewave_vector

YDSE Bright Fringes Position

xn=nλDdx_n = \frac{n\lambda D}{d}

Linear position of constructive interference fringes on the screen in YDSE.

applies whenD≫dD \gg d, small angles.
interferenceydsemaxima

YDSE Dark Fringes Position

xn=(n+12)λDdx_n = \left(n + \frac{1}{2}\right)\frac{\lambda D}{d}

Linear position of destructive interference fringes on the screen in YDSE.

applies whenD≫dD \gg d, small angles.
interferenceydseminima

Optical Path Phase Shift due to Slab

Δϕ=2πλ(μ−1)t\Delta \phi = \frac{2\pi}{\lambda}(\mu - 1)t

Extra phase difference introduced by a transparent slab in the path.

interferenceydseslabphasejee-advanced

Fringe Shift due to Glass Slab

Δxshift=Dd(μ−1)t\Delta x_{shift} = \frac{D}{d}(\mu - 1)t

Lateral shift of the entire interference pattern when a slab of thickness t is inserted before one slit.

interferenceydseslabjee-advanced

Fringe Width in YDSE

β=λDd\beta = \frac{\lambda D}{d}

Distance between two consecutive bright or dark fringes.

applies whenD≫dD \gg d, small angles.
interferenceydsefringe_width
07

Diffraction

4 formulas

Linear Width of Central Maximum

W=2λDaW = \frac{2\lambda D}{a}

Linear span of the central maximum on a screen at distance D.

applies whenSmall angle approximation.
diffractioncentral_widthlinear

Angular Width of Central Maximum

2θ=2λa2\theta = \frac{2\lambda}{a}

Total angular spread of the central bright fringe.

applies whenSmall angle approximation.
diffractioncentral_width

Single Slit Secondary Maxima

asin⁡θ≈(n+12)λa \sin\theta \approx \left(n + \frac{1}{2}\right)\lambda

Approximate angular positions of secondary bright fringes in diffraction.

applies whenn=±1,±2,…n = \pm 1, \pm 2, \dots
diffractionsingle_slitmaxima

Single Slit Minima

asin⁡θ=nλa \sin\theta = n\lambda

Condition for dark fringes in single slit diffraction.

applies whenn=±1,±2,…n = \pm 1, \pm 2, \dots (n≠0n \neq 0)
diffractionsingle_slitminima
08

Polarisation

3 formulas

Brewster's Law

tan⁡ip=n21\tan i_p = n_{21}

Angle of incidence at which the reflected light is completely plane-polarized.

applies whenReflected and refracted rays are orthogonal.
polarisationbrewster

Malus' Law

I=I0cos⁡2θI = I_0 \cos^2\theta

Intensity of linearly polarized light after passing through an analyzer at angle theta.

applies whenIncident light is perfectly polarized.
polarisationmaluspolaroid

Intensity Through Three Polaroids

I=I04sin⁡2(2θ)I = \frac{I_0}{4} \sin^2(2\theta)

Intensity when a third polaroid is inserted at angle theta between two crossed polaroids.

applies whenFirst and third polaroids are crossed (90∘90^{\circ}).
polarisationmaluspolaroidjee-advanced
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